When you look at the mirror, you feel that your right hand is the left hand of the mirror-self. You exchange perspectives. But before that, how do you recognize that the person in the mirror is yourself?
You must recognize that the body you feel here through proprioception is equivalent to the body you see there in the mirror.
Animal psychologists say that adult chimpanzees recognizes that the figure in the mirror is him/herself within few hours. It seems that they have their own body image in their mind.
But it is also said that the chimps grown up alone without other chimps don't come to recognize themselves in the mirror.
So, it is possible to speculate that the other individuals body plays a crucial role to create the body image in the mind. Probably we need the other's body to see our own body from third person's perspective and to construct our own body image in the mind.